Gengar seems to be based off a distorted shadow with traits of cartoonish ghosts and cats. It's smile and concepts could also have been influenced by the Cheshire Cat.
Gengar is well-known by many for it's appearance in the anime episode, The Tower of Terror, where it, Haunter, and Gastly took delight into messing around with Ash and his companions, as well as Team Rocket.
Anime aside, Gengar has it's uses competitively. It has a strong 130 base Sp. Atk stat, along with a good speed stat to back it up, which can help it deal good damage. Before Generation IV's physical/special split, Gengar can take advantage of it's monstrous Sp. Atk to effectively use the Elemental Punches (Fire Punch, ThunderPunch, and Ice Punch.) in battle.
From Generation IV onwards due to the physical/special split, Gengar is now able to run STAB Shadow Ball effectively, as it is now classified as a special attack. Before Gen IV, all Ghost Type attacks were considered physical. Gengar can even learn Focus Blast to get past Steel and Dark Types in Gen IV.
Since Generation VI introduced the Fairy Type, Gengar can now take advantage of another STAB special move, Sludge Bomb, which was only useful against Grass Types in the past. Gengar even gets a Mega Evolution in X/Y, which gifted it the Shadow Tag Ability.
Although it loses it's immunity to Ground due to losing Levitate, Mega Gengar can now effectively use the Perish Trap combo. With a Speed stat on par with Mewtwo, combined with White Kyurem's gnarly Sp. Atk stat, Mega Gengar was banned straight to Ubers by Smogon.
In general, Gengar is a well-respected special sweeper who can also have a few tricks up in it's battling sleeve.